Music & math quiz

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You are writing a piece of music in which you will play 1, 2, 3, etc. to 10 beats per measure at the same time. Your music notation program only supports triplets as the only 'not a multiple of 2 to an integer power' tuple and multiple staves. How many beats per measure must your time signature have?

The problem would simply be find the LCD of the numbers 1-10 if only notes of one duration were allowed and you simply tied the correct number of them together to produce a note whose duration was 1 / nth of a beat. However, the procedure for splitting a note has been in musical notation for centuries: add a stem to a whole note, fill in a half note, add a(nother) flag to split quarters, eighths, etc. Also, triplets are supported so it won't be necessary to come up with an LCD of 2520.

While 2025 is the LCD for 1-10, none of the 2's and only one of the 3's are needed.
2025/(2*2*2*3) = 105. With a time signature of 105/8, divide the number of beats any one staff will have into 105 to get the number of 8th notes needed. That can be divided by 8 to get the number of whole notes needed.

For 1 to a bar, 13 whole notes plus one 8th note tied together will do it. For 2/measure, 6 wholes, a half, and 16th will do it. For 6 to a bar: 2 wholes plus dotted 8th. For 9 to a bar copy the 6 to a bar to it and copy the first three beats to the end of the measure--then turn the whole bar into a triplet.